Missile Aerodynamics Model Learning through Center- of- Pressure Estimation based on a Dynamics-embedded Neural-ODE

The control performance of aerospace systems such as missiles highly depends on the accuracy of aerodynamic models. In particular, uncertainties in the center-of-pressure (CP) can significantly degrade stability due to their direct influence on aerodynamic moments. Conventional statistical or data-driven models often show limited interpolation capabilities and lack physical consistency. Therefore, this study proposes a dynamics-embedded neural ordinary differential equation framework to estimate nonlinear CP errors. The method models only the uncertain CP error with a neural network while explicitly embedding it within rigid-body dynamics. An integral-form loss function is introduced to capture the temporal characteristics of flight data and, enhance noise robustness and data efficiency. Validation using high-fidelity, six degrees-of-freedom simulation data demonstrates that the proposed model accurately identifies nonlinear CP errors and generalizes well to unseen flight conditions. Moreover, it produces smooth and physically consistent interpolation in data-sparse regions, indicating that the model learns intrinsic physical relationships rather than memorizing trajectories. This work presents a dynamics-embedded learning framework that combines analytical dynamics with neural modeling, providing a reliable and interpretable approach for aerodynamic uncertainty estimation in complex aerospace systems.